Question

1. (Fracture toughness) (a) An AISI 4340 steel plate has a width W of 30 cm and has a central crack 2a of 3 mm. The plate is under a uniform stress, ?·This steel has a Kic value of 50 m2. Find the maximum stress for this crack length. (b) If the operating stress is 1500 MPa, compute the maximum crack size that the steel may have without failure. 2. (Plastic zone radius) The size of the plastic zone at the crack tip in the general plane stress case is given by ,2 cos 3cos2e 4 (a) Determine the radius if the plastic zone in the direction of the crack. (b) Determine the angle ? at which the plastic zone is largest. 3. (Crack extension force) A sheet of polystyrene has a thin central crack with 2a 50 mm. The crack propagates catastrophically at an applied stress of 10 MPa Young's modulus polystyrene is 3.8 GPa, and the Poisson's ratio is 0.4. Find Gle.

Deformation and Fracture Mechanics

Answer 1

1.

Ans:

2. - 1 XI 150 =50X1 Up kmoo the ΟΧΙ。 X ( = 구28 (b) Givey 。一 1500 .MPa- SO = 3.5363 X 104 meter

2.

Ans:

The radius of the plastic zone in the direction of the crack can be determined by evaluating the given equation for $\theta=0$ . $r_y=\frac{K_l^2}{2\pi \sigma _y^2}$

b) Determine the angle at which the plastic zone is the largest, is a matter of finding a maximum for that equation

dry d (2K2 0 3K2 (2cos --3cos*-) 2K2 (2cos 2(-sino) + 6cos3@sin2)-K2(-sine, 3sinecos2@) -sine 3sinecos)

$\frac{dr_y}{d\theta }=\frac{K_l^2}{\pi \sigma _y^2}(-sin\theta+3sin\theta cos^2\frac{\theta}{2} )$

dr de

$1=3 cos^2\frac{\theta}{2}$

cos2
$\sqrt{ \frac{1}{3}}= cos\frac{\theta}{2}\rightarrow \theta=2cos^{-1}(\sqrt{ \frac{1}{3}})$

θ = 109.47 deg

3.

Ans:

Sol = 0.4 IC 2. 2 O x IUD